Derivation of a Poroelastic Flexural Shell Model
Derivation of a Poroelastic Flexural Shell Model
复制标题
多孔弹性弯曲壳模型的推导
DOI：
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发表时间：
2015
影响因子：
1.6
通讯作者：
J. Tambača
中科院分区：
文献类型：
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作者：
A. Mikelić;J. Tambača
本文研究了多孔弹性弯曲薄壳中准静态毕奥方程解在薄壳厚度趋于零时的极限行为，推广了Marciniak-Czochra和Mikelic在[Arch. Ration.机械肛门，215（2015），pp. 1035- 1062]。我们选择了与壳体厚度相对应的太扎吉时间，并获得了三维固体位移、流体压力和总孔隙弹性应力对新一类壳体方程解的强收敛性。导出的弯曲方程与压力方程耦合，并且它包含由于孔隙压力沿壳体厚度的变化而引起的弯矩。有效压力方程仅在法向为抛物线型。作为附加项，它包含中间表面弯曲应变的时间导数。该模型的推导是经典线弹性壳推导结果的推广。
In this paper we investigate the limit behavior of the solution to quasi-static Biot equations in thin poroelastic flexural shells as the thickness of the shell tends to zero and extend the results obtained for the poroelastic plate by Marciniak-Czochra and Mikelic in [Arch. Ration. Mech. Anal., 215 (2015), pp. 1035--1062]. We choose Terzaghi's time corresponding to the shell thickness and obtain the strong convergence of the three-dimensional solid displacement, fluid pressure, and total poroelastic stress to the solution of the new class of shell equations. The derived bending equation is coupled with the pressure equation, and it contains the bending moment due to the variation in pore pressure across the shell thickness. The effective pressure equation is parabolic only in the normal direction. As an additional term it contains the time derivative of the middle-surface flexural strain. Derivation of the model presents an extension of the results on the derivation of classical linear elastic shells by ...